List of top Questions asked in CUET (PG)- 2026

Orthogonal projection of $\vec{v}$ on $\vec{a}$ is

Let $c$ be boundary of $[0, 1] \times [0, 1]$ oriented counter clockwise then $\int_c (y^4 + x^3) dx + 2 x^6 dy$ is

Let $\vec{F}(x, y, z) = x \hat{i} + x y \hat{j} + \hat{k}$, then $\text{curl}(\vec{F})$ is

The value of $\vec{\nabla}\left(\frac{f}{g}\right)$ at points where $g(x) \neq 0$ is given by

Let $\vec{F} = y e^z \hat{i} + x e^z \hat{j} + x y e^z \hat{k}$, then integral of $\vec{F}$ around the boundary of oriented surface $S$ is

Let $\vec{F}(x, y, z) = x^2 y \hat{i} + z \hat{j} + x y z \hat{k}$, then $\text{div} \vec{F}$ is given by

The integrating factor of the differential equation $(e^x - \sin y) dx + \cos y \, dy = 0$ is

The solution of the differential equation $(2 \cos y) y' + \sin y = x^2 \csc y, y \neq 0$ is:

A solution of the differential equation $(D^2 - 1)y = 2^x + e^{-x}; D = \frac{d}{dx}$ is

The set of linearly independent solutions of the differential equation $(D^4 - D^3)y = 0; D = \frac{d}{dx}$ is

Let $u, v$ and $w$ be the non-zero solutions of the differential equation
\[ (D^3 - 6D^2 + 11D - 6)y = 0; \quad D = \frac{d}{dx} \] Then the Wronskian of $u, v$ and $w$ is

The value of $\iiint_B (x + 2y + 3z)^2 \, dx \, dy \, dz$ is, where $B$ is the box $[0, 1] \times \left[-\frac{1}{2}, 0\right] \times \left[0, \frac{1}{3}\right]$

A solution curve of the equation $x y' = 2y$ passing through $(1, 4)$, also passes through

Consider the differential equation
\[ y'' - 4y' + 20y = 0 \] with $y\left(\frac{\pi}{2}\right) = 0$, and $y'\left(\frac{\pi}{2}\right) = 1$, then the value of $y\left(\frac{\pi}{8}\right)$ is

The value of $\iint_S \cos(x) \sin(y) \, dx \, dy$ is, where $S$ is $\left[0, \frac{\pi}{2}\right] \times \left[0, \frac{\pi}{2}\right]$

Let $f(x, y) = x^2 + y^2$ and $R = [-1, 1] \times [0, 1]$, then $\iint_R f(x, y) \, dx \, dy$ is

If $f_1$ and $f_2$ are integrable on the region $R$ in the plane $\mathbb{R}^2$ and if $f_1(x, y) \leq f_2(x, y)$ for all $(x, y)$ in $R$ then which of the following always hold:

Let $f(z)$ be continuous in a simply connected region $G$ and suppose $\oint_c f(z)dz = 0$ around every simple closed curve $c$. Then

Which of the following function is analytic on $\mathbb{C}$

If $f(z) = \frac{z}{\bar{z}}$, then $\lim_{z \to 0} f(z)$

If $f'(z) = 0$ everywhere in a connected open set $G \subset \mathbb{C}$, then $f(z)$ is

Which of the following function satisfies Cauchy-Riemann equations:

Every bounded entire function is constant. This theorem is known as:

Let $A = \{1, 2, 3\}$ and $B = \{a, b\}$ then number of relations from set $A$ to set $B$ are

Let $A$ and $B$ be two sets having $m$ and $n$ elements respectively, then total number of functions from $A$ to $B$ are